A note on the quadratic convergence of the inexact Newton methods
Abstract We show that a new sufficient condition for the convergence with q-order two of the inexact Newton iterates may be…
Numerical Analysis
On the high convergence orders of the Newton-GMBACK methods
Abstract GMBACK is a Krylov solver for linear systems in \(\mathbb{R}^n\). We analyze here the high convergence orders (superlinear convergence)…
On an Aitken-Newton type method
Abstract We study the solving of nonlinear equations by an iterative method of Aitken type, which has the interpolation nodes…
On a Newton-Steffensen type method
Abstract In this paper we study the convergence of a Newton-Steffensen type method for solving nonlinear equations in R, introduced by…
On a robust Aitken-Newton method based on the Hermite polynomial
Abstract We introduce an Aitken–Newton iterative method for nonlinear equations, which is obtained by using the Hermite inverse interpolation polynomial…
Bilateral approximations for some Aitken-Steffensen-Hermite type methods of order three
Abstract We study the local convergence of some Aitken–Steffensen–Hermite type methods of order three. We obtain that under some reasonable…
A unified treatment of the modified Newton and chord methods
Abstract The aim of this paper is to obtain a unified treatment of some iterative methods. We obtain some conditions…
On a Steffensen-Hermite method of order three
Abstract In this paper we study a third order Steffensen type method obtained by controlling the interpolation nodes in the…
On a Steffensen type method
Abstract We study a general Steffensen type method based on the inverse interpolation Lagrange polynomial of second degree. We show…
Bilateral approximations of solutions of equations by order three Steffensen-type methods
Abstract We study the convergence of a method of Steffensen-type, which is obtained from the Lagrange polynomial of inverse interpolation with…